A Partially Backlogged Inventory Model with Ramp Type Demand and Time Dependent Holding Cost

The presented paper delves into a mathematical model incorporating assumptions of the widely observed ramp-type demand and dynamic holding costs contingent upon time. The holding cost is increasing linear function of time at the beginning of the cycle and after a while it becomes constant. The deterioration rate has been assumed as a time varying function of time. Moreover, the shortages are occurred and backlogged in partial nature. The goal of the proposed paper is to derive optimal policy and minimize the total inventory cost. The total cost is convex function, and it has been presented graphically and a numerical example has been solved. Sensitivity analysis has been conducted to assess the impact of various parameters considered in the study, providing support for the model in a realistic environment.